{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Variational Quantum Time Evolution\n",
        "This notebook demostrates how to use Qiskit’s implementation of the Variational Quantum Time Evolution (VarQTE) algorithm for computing the time evolving state under a given Hamiltonian. Specifically, it introduces variational quantum imaginary and real time evolution based on McLachlan's variational principle, and shows how this can be leveraged using the `algorithms.time_evolvers.variational` sub-module."
      ],
      "metadata": {
        "id": "lTiEsmieVAf-"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zw5nQ9h0xVqF"
      },
      "source": [
        "## Introduction\n",
        "`VarQTE` is a quantum algorithm that simulates the time evolving state under given Hamiltonian ([Yuan et al. Quantum 3, 191](https://quantum-journal.org/papers/q-2019-10-07-191/)). For a quantum closed system's Hamiltonian $H$, the time evolving $\\rho$ density matrix follows the equation below\n",
        "\n",
        "$$\\frac{d\\rho}{dt}=\\mathcal{L}\\left(\\rho\\right)$$\n",
        "\n",
        "where $\\mathcal{L}\\left(\\rho\\right)=-i[H,\\rho]$ for real time dynamics and $\\mathcal{L}\\left(\\rho\\right)=-[H,\\rho]$ for imaginary time dynamics. The corresponding state $\\psi[\\theta(t)]$ is parameterized by time dependent $\\theta(t)$. Using McLachlan variational principle, the algorithm updates the parameters by minimizing the distance between the right hand side and left hand side of the equation above. This is called the McLachlan's distance $L$ , and defined as\n",
        "\n",
        "$$L\\equiv\\left\\Vert \\sum_{i}\\frac{\\partial\\rho\\left[\\theta\\right]}{\\partial\\theta_{i}}\\dot{\\theta}_{i}-\\mathcal{L}\\left(\\rho\\right)\\right\\Vert _{F}$$\n",
        "\n",
        "where $\\left\\Vert M\\right\\Vert _{F}=\\sqrt{M^{\\dagger}M}$ is the Frobenius norm of the matrix $M$. The equivalent way is to minimize the squared distance\n",
        "\n",
        "$$\\left\\Vert \\sum_{i}\\frac{\\partial\\rho\\left[\\theta\\right]}{\\partial\\theta_{i}}\\dot{\\theta}_{i}-\\mathcal{L}\\left(\\rho\\right)\\right\\Vert _{F}^{2}=\\sum_{i,j}F_{ij}\\dot{\\theta}_{i}\\dot{\\theta}_{j}-2\\sum_{i}V_{i}\\dot{\\theta}_{i}+\\text{Tr}\\left[\\mathcal{L}^{2}\\left(\\rho\\right)\\right]$$\n",
        "\n",
        "where\n",
        "\n",
        "$$F_{ij}=2\\text{Re}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{j}}+\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}\\left|\\psi\\left[\\theta\\right]\\right\\rangle \\left\\langle \\psi\\left[\\theta\\right]\\right|\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{j}}\\right]$$,\n",
        "\n",
        "and\n",
        "\n",
        "$$V_{i}=\\begin{cases}\n",
        "2\\text{Im}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}H\\left|\\psi\\left[\\theta\\right]\\right\\rangle +\\left\\langle \\psi\\left[\\theta\\right]\\right|\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{i}}\\left\\langle H\\right\\rangle _{\\theta}\\right] & \\text{Real time}\\\\\n",
        "2\\text{Re}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}H\\left|\\psi\\left[\\theta\\right]\\right\\rangle \\right] & \\text{Imaginary time}\n",
        "\\end{cases}$$.\n",
        "\n",
        "Minimizing $L^2$ with respect to $\\dot{\\theta}$ can lead to the equation of motion for $\\theta$\n",
        "\n",
        "$$\\sum_{ij}F_{ij}\\dot{\\theta}_{i}=V_{j}$$\n",
        "\n",
        "Solving this equation is equivalent to minimizing $L^2$, a variational approach that is more stable in simulation ([Yuan et al. Quantum 3, 191](https://quantum-journal.org/papers/q-2019-10-07-191/)). $F_{i,j}$ and $V_{j}$ can be calculated using a quantum circuit (more details in [Zoufal et al.](https://arxiv.org/abs/2108.00022) and [Yao et al.](https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.030307)), and the classical computer can minimize $L^2$ to get the variational parameters for the next time step.\n", 
        "In this tutorial, we focus on how to use Qiskit's implementation of the `VarQTE` algorithm.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Running VarQTE"
      ],
      "metadata": {
        "id": "caoBgyluhQ3L"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this tutorial, we will use two Qiskit classes that extend `VarQTE`, `VarQITE` ([Variational Quantum Imaginary Time Evolution](https://qiskit.org/documentation/stubs/qiskit.algorithms.VarQITE.html#qiskit.algorithms.VarQITE)) and `VarQRTE` ([Variational Quantum Real Time Evolution](https://qiskit.org/documentation/stubs/qiskit.algorithms.VarQRTE.html#qiskit.algorithms.VarQRTE)) for time evolution.\n",
        "We can use a simple Ising model on a spin chain to illustrate this. Let us consider the following Hamiltonian:\n",
        "\n",
        "$$H = -J\\sum_{i=0}^{L-2}Z_{i}Z_{i+1} - h\\sum_{i=0}^{L-1}X_i$$\n",
        "\n",
        "where $J$ stands for the interaction energy, and\n",
        "$h$ represents an external field which is orthogonal to the transverse direction. $Z_i$ and $X_i$ are the Pauli operators on the spins. Taking $L=2$, $J=0.2$,  and $h =1$, the Hamiltonian and the magnetization $\\sum_i Z_i$ can be constructed using `SparsePauliOp` as follows:"
      ],
      "metadata": {
        "id": "WG-18slyLnVM"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "6B0nZEDh0EqI"
      },
      "outputs": [],
      "source": [
        "from qiskit.quantum_info import SparsePauliOp\n",
        "\n",
        "hamiltonian = SparsePauliOp(['ZZ',  'IX', 'XI'],\n",
        "              coeffs=[-0.2 , -1, -1])\n",
        "\n",
        "magnetization = SparsePauliOp([ 'IZ', 'ZI'], coeffs=[1, 1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y_9Jskw4m8nF"
      },
      "source": [
        "# Imaginary Time Evolution\n",
        "\n",
        "Imaginary time evolution can be used, for example, to find the ground state or calculate the finite temperature expectation value of the system. Here, we will use the `VarQITE` class from `algorithms.time_evolvers.variational` to compute a ground state energy. Firstly, we need to choose an ansatz. We can use `EfficientSU2` to easily construct an ansatz, setting the number of repetitions using `reps`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        },
        "id": "0fyXDwr10KqA",
        "outputId": "8df79033-2b4e-40cc-96a4-081300d579a9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 538.128x200.667 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "from qiskit.circuit.library import EfficientSU2\n",
        "\n",
        "ansatz = EfficientSU2(hamiltonian.num_qubits, reps=1)\n",
        "ansatz.decompose().draw('mpl')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TZEbbCfg_JLq"
      },
      "source": [
        "Here, we prepare a dictionary to store the initial parameters we set up, which determine the initial state."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "Ju2SO4sZ0R3P"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "init_param_values={}\n",
        "for i in range(len(ansatz.parameters)):\n",
        "    init_param_values[ansatz.parameters[i]]=np.pi/2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2VzjiBc0EeRb"
      },
      "source": [
        "Note that the initial state should be in overlap with the ground state.\n",
        "\n",
        "Next, we choose `ImaginaryMcLachlanPrinciple` as the variational principle we'll use later."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "zK934ZfdEJtG"
      },
      "outputs": [],
      "source": [
        "from qiskit.algorithms.time_evolvers.variational import ImaginaryMcLachlanPrinciple\n",
        "\n",
        "var_principle = ImaginaryMcLachlanPrinciple()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4gOIKzLYFaCP"
      },
      "source": [
        "We set a target imaginary time $t=5$, and set the Hamiltonian as an auxiliary operator. We create  a `TimeEvolutionProblem` instance with `hamiltonian`, `time`, and `aux_operators` as arguments."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "_4LN_OIB0Vn0"
      },
      "outputs": [],
      "source": [
        "from qiskit.algorithms import TimeEvolutionProblem\n",
        "\n",
        "time = 5.0\n",
        "aux_ops = [hamiltonian]\n",
        "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bhGjcZzsGcFa"
      },
      "source": [
        "We now use the `VarQITE` class to calculate the imaginary time evolving state. We can use `VarQITE.evolve` to get the results. Note this cell may take around  $1.5$  minutes to finish."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "T2jv73lRGbHt"
      },
      "outputs": [],
      "source": [
        "from qiskit.algorithms import VarQITE\n",
        "from qiskit.primitives import Estimator\n",
        "\n",
        "var_qite = VarQITE(ansatz, init_param_values, var_principle, Estimator()) \n",
        "# an Estimator instance is necessary, if we want to calculate the expectation value of auxiliary operators.\n",
        "evolution_result = var_qite.evolve(evolution_problem)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5oFggUXMktgG"
      },
      "source": [
        "## Exact Classical Solution\n",
        "In order to check whether our calculation using `VarQITE` is correct or not, we also call `SciPyImaginaryEvolver` to help us calculate the exact solution.\n",
        "\n",
        "Firstly, we can use `qiskit.quantum_info.Statevector` to help us get the statevector from the quantum circuit."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "nF6lJqEZkz2f"
      },
      "outputs": [],
      "source": [
        "from qiskit.quantum_info import Statevector\n",
        "\n",
        "init_state = Statevector(ansatz.assign_parameters(init_param_values))"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Then we can set up the evolving problem using `SciPyImaginaryEvolver`. Here we set number of time steps as $501$."
      ],
      "metadata": {
        "id": "SUWse0TNkfky"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.algorithms import SciPyImaginaryEvolver\n",
        "\n",
        "evolution_problem = TimeEvolutionProblem(hamiltonian, time, initial_state=init_state, aux_operators=aux_ops)\n",
        "exact_evol = SciPyImaginaryEvolver(num_timesteps=501)\n",
        "sol = exact_evol.evolve(evolution_problem)"
      ],
      "metadata": {
        "id": "ZX89FSpmkhd7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "afbae447lVAR"
      },
      "source": [
        "## Results and Comparison\n",
        "\n",
        "We use `evolution_result.observables` to get the variation over time of the expectation values of the Hamiltonian."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "cCWhV-2y765c",
        "outputId": "5562be51-75fa-4a4e-a4dc-292c2d9b22f6"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import pylab\n",
        "\n",
        "h_exp_val = np.array([ele[0][0] for ele in evolution_result.observables])\n",
        "\n",
        "exact_h_exp_val = sol.observables[0][0].real\n",
        "\n",
        "times = evolution_result.times\n",
        "pylab.plot(times, h_exp_val, label= \"VarQITE\")\n",
        "pylab.plot(times, exact_h_exp_val , label= \"Exact\",  linestyle='--')\n",
        "pylab.xlabel(\"Time\")\n",
        "pylab.ylabel(r\"$\\langle H \\rangle$ (energy)\")\n",
        "pylab.legend(loc=\"upper right\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-2uSBEO83vU3",
        "outputId": "369b4864-f0b0-4096-8a59-4d104bf841b1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ground state energy -2.0097479079521197\n"
          ]
        }
      ],
      "source": [
        "print(\"Ground state energy\", h_exp_val[-1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8dp41GBm3TIS"
      },
      "source": [
        "As the above figure indicates, we have obtained the converged ground state energy."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zSGo5QcUlePi"
      },
      "source": [
        "## Efficient classical calculation of gradients with VarQITE\n",
        "\n",
        "You can use classically efficient gradient calculations to speed up the time evolution simulation by setting `qgt` to `ReverseQGT()` and `gradient` to `ReverseEstimatorGradient()`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "6PzxWQyIld-T"
      },
      "outputs": [],
      "source": [
        "from qiskit.algorithms.gradients import ReverseEstimatorGradient, ReverseQGT\n",
        "\n",
        "var_principle = ImaginaryMcLachlanPrinciple(qgt = ReverseQGT() , gradient = ReverseEstimatorGradient())\n",
        "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n",
        "var_qite = VarQITE(ansatz, init_param_values, var_principle, Estimator())\n",
        "evolution_result_eff = var_qite.evolve(evolution_problem)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S8mtNpT5NirQ"
      },
      "source": [
        "In this example, it takes only $1$ minute to calculate imaginary time evolution. The execution time is reduced by about 33% (this may vary for each execution, but generally results in a speedup)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "pvmRXMXxBz2H",
        "outputId": "11962fe6-96d6-4aa4-c4b4-6fcbbf65515d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "h_exp_val_eff = np.array([ele[0][0] for ele in evolution_result_eff.observables])\n",
        "\n",
        "exact_h_exp_val_eff = sol.observables[0][0].real\n",
        "\n",
        "times = evolution_result_eff.times\n",
        "pylab.plot(times, h_exp_val_eff, label= r\"VarQITE$_{eff}$\")\n",
        "pylab.plot(times, exact_h_exp_val_eff , label= \"Exact\",  linestyle='--')\n",
        "pylab.xlabel(\"Time\")\n",
        "pylab.ylabel(r\"$\\langle H \\rangle$ (energy)\")\n",
        "pylab.legend(loc=\"upper right\");"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can also get a converged result, which is consistent with the previous one."
      ],
      "metadata": {
        "id": "3yZ_CTqK0-Oy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Ground state energy\", h_exp_val_eff[-1])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_OxkX7wv03db",
        "outputId": "04a87fdc-e2e0-4cb6-eb96-1c6e9057d28f"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ground state energy -2.0097479079521183\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ed9_4HhXLE_A"
      },
      "source": [
        "\n",
        "\n",
        "Let us compare the performance of different methods. The error is defined as the difference between the results and exact solution for each method."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "PpDLxpZdpFhA",
        "outputId": "7d7acfef-27f8-47fa-c464-4ab0e15a4267"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "pylab.plot(times, (h_exp_val-exact_h_exp_val), label= \"VarQITE\")\n",
        "pylab.plot(times, (h_exp_val_eff-exact_h_exp_val_eff), label= r\"VarQITE$_{eff}$\",  linestyle='--')\n",
        "pylab.xlabel(\"Time\")\n",
        "pylab.ylabel(r\"$\\Delta \\langle H \\rangle$\")\n",
        "pylab.legend(loc=\"upper right\");"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ejlBv7Qi0C1-"
      },
      "source": [
        "In this task, the accuracies of `VarQITE` with both gradient methods are very close, but `ReverseEstimatorGradient()` takes a considerably shorter time to run. \n",
        "\n",
        "We can do the same comparison for `VarQRTE` for simulating the magnetization of the Ising model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m-tp9kdHmy55"
      },
      "source": [
        "# Real Time Evolution\n",
        "Real time evolution is more suitable for tasks such as simulating quantum dynamics. For example, one can use `VarQRTE` to get time evolving expectation values of the magnetization.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TPGhF7xfodnT"
      },
      "source": [
        "## VarQRTE\n",
        "Again, the first step is to select an ansatz."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        },
        "id": "l7hz6wSLnZx3",
        "outputId": "b23ea3f0-d19c-4def-a494-72fa0d5d40cf"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 538.128x200.667 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "ansatz = EfficientSU2(hamiltonian.num_qubits, reps=1)\n",
        "ansatz.decompose().draw('mpl')"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We set all initial parameters as $\\frac{\\pi}{2}$."
      ],
      "metadata": {
        "id": "Hil3c_xfubIw"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "thWw2mahnipB"
      },
      "outputs": [],
      "source": [
        "init_param_values = {}\n",
        "\n",
        "for i in range(len(ansatz.parameters)):\n",
        "    init_param_values[ansatz.parameters[i]] = np.pi/2 # initialize the parameters which also decide the initial state"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We also define an initial state:"
      ],
      "metadata": {
        "id": "i18irpxD4ETl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "init_state = Statevector(ansatz.assign_parameters(init_param_values))\n",
        "print(init_state)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4AsVk0Gj3-KQ",
        "outputId": "60460d22-a873-4c1c-a034-a5b62c305526"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Statevector([-5.00000000e-01+0.00000000e+00j,\n",
            "             -5.00000000e-01-5.55111512e-17j,\n",
            "              0.00000000e+00-5.00000000e-01j,\n",
            "              1.66533454e-16+5.00000000e-01j],\n",
            "            dims=(2, 2))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In order to use the real time McLachlan principle, we instantiate the `RealMcLachlanPrinciple` class."
      ],
      "metadata": {
        "id": "-ee7tApy4lsp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.algorithms.time_evolvers.variational import RealMcLachlanPrinciple\n",
        "\n",
        "var_principle = RealMcLachlanPrinciple()"
      ],
      "metadata": {
        "id": "U8ytm_9g4kkx"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qknpQG8LFRdX"
      },
      "source": [
        "We also set the target time as $t=10$, and set the auxiliary operator to be the magnetization operator. The following steps are similar to `VarQITE`.\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "aux_ops = [magnetization]"
      ],
      "metadata": {
        "id": "Yh7vyZr62ubD"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "-o2B3533nqsU"
      },
      "outputs": [],
      "source": [
        "from qiskit.algorithms import VarQRTE\n",
        "\n",
        "time = 10.0\n",
        "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n",
        "var_qrte = VarQRTE(ansatz, init_param_values,var_principle, Estimator())\n",
        "evolution_result_re = var_qrte.evolve(evolution_problem)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can also obtain the exact solution with `SciPyRealEvolver`. We first create the corresponding initial state for the exact classical method."
      ],
      "metadata": {
        "id": "ByiDyBuia1fN"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "yDWL-Zd5oQwH"
      },
      "outputs": [],
      "source": [
        "init_circ = ansatz.assign_parameters(init_param_values)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "`SciPyRealEvolver` can help us get the classical exact result."
      ],
      "metadata": {
        "id": "SimuqpjpbHuU"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "ac4twWUqonXm"
      },
      "outputs": [],
      "source": [
        "from qiskit.algorithms import SciPyRealEvolver\n",
        "\n",
        "evolution_problem = TimeEvolutionProblem(hamiltonian, time, initial_state = init_circ, aux_operators=aux_ops)\n",
        "rtev = SciPyRealEvolver(1001)\n",
        "sol = rtev.evolve(evolution_problem)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can compare the results, where $m_z$ represents the magnetization."
      ],
      "metadata": {
        "id": "M2hl_f2Y67tu"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "02oeqzHDotYT",
        "outputId": "2b95d596-f9be-43cc-f1f0-18c1f13dc47d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "mz_exp_val_re = np.array([ele[0][0] for ele in evolution_result_re.observables])\n",
        "exact_mz_exp_val_re = sol.observables[0][0].real\n",
        "times = evolution_result_re.times\n",
        "pylab.plot(times, mz_exp_val_re, label= \"VarQRTE\")\n",
        "pylab.plot(times, exact_mz_exp_val_re , label= \"Exact\",  linestyle='--')\n",
        "pylab.xlabel(\"Time\")\n",
        "pylab.ylabel(r\"$\\langle m_z \\rangle$\")\n",
        "pylab.legend(loc=\"upper right\");"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Efficient Way to run VarQRTE\n",
        "\n",
        "Similarly, we can set `qpt` as `ReverseQGT()` and `gradient` as `ReverseEstimatorGradient()` to speed up the calculation."
      ],
      "metadata": {
        "id": "korN4ZZv8j_8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "var_principle = RealMcLachlanPrinciple(qgt = ReverseQGT() , gradient = ReverseEstimatorGradient())\n",
        "time = 10.0\n",
        "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n",
        "var_qrte = VarQRTE(ansatz, init_param_values,var_principle, Estimator())\n",
        "evolution_result_re_eff = var_qrte.evolve(evolution_problem)"
      ],
      "metadata": {
        "id": "gnBS19NQ85cn"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "mz_exp_val_re_eff = np.array([ele[0][0] for ele in evolution_result_re_eff.observables])\n",
        "pylab.plot(times, mz_exp_val_re_eff, label= r\"VarQRTE$_{eff}$\")\n",
        "pylab.plot(times, exact_mz_exp_val_re , label= \"Exact\",  linestyle='--')\n",
        "pylab.xlabel(\"Time\")\n",
        "pylab.ylabel(r\"$\\langle m_z \\rangle$\")\n",
        "pylab.legend(loc=\"upper right\");"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "IriOFWu89iTX",
        "outputId": "1160c308-3d08-490f-a595-325433794117"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Again, the accuracies of `VarQRTE` with both gradient methods are very similar, while the `ReverseEstimatorGradient()` shows a speedup of about $21\\%$ in this execution."
      ],
      "metadata": {
        "id": "-IHBehQVAfZm"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "ESuUu7jILMQn",
        "outputId": "e3f76d34-ef66-47d8-f4a4-9f20713ba8e7"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "pylab.plot(times, (mz_exp_val_re-exact_mz_exp_val_re), label= \"VarQRTE\")\n",
        "pylab.plot(times, (mz_exp_val_re_eff-exact_mz_exp_val_re), label= r\"VarQRTE$_{eff}$\",  linestyle='--')\n",
        "pylab.xlabel(\"Time\")\n",
        "pylab.ylabel(r\"$\\Delta \\langle m_z \\rangle$\")\n",
        "pylab.legend(loc=\"upper right\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 555
        },
        "id": "tFR-8_hIvuwz",
        "outputId": "d9c1cc74-52e6-47be-e57c-26e032104636"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.24.1</td></tr><tr><td><code>qiskit-aer</code></td><td>0.12.0</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.20.2</td></tr><tr><td><code>qiskit</code></td><td>0.43.1</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.10.12</td></tr><tr><td>Python compiler</td><td>GCC 9.4.0</td></tr><tr><td>Python build</td><td>main, Jun  7 2023 12:45:35</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>1</td></tr><tr><td>Memory (Gb)</td><td>12.678398132324219</td></tr><tr><td colspan='2'>Fri Jun 16 00:10:15 2023 UTC</td></tr></table>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>&copy; Copyright IBM 2017, 2023.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "import qiskit.tools.jupyter\n",
        "%qiskit_version_table\n",
        "%qiskit_copyright"
      ]
    }
  ],
  "metadata": {
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